The performance and efficiency of the distributed database system (DDBS) design are dependent on proper data fragmentation, reallocation, and replication of global relations. In this research, a Cluster Based Distributed and Parallel Database System (CB-DDBS) architecture over a cloud environment is proposed. The proposed CB-DDBS architecture processes the client's query requests, which access the clustered DDBS from anywhere. It also allows vertical and horizontal fragmentation, allocation, and replication decisions to be taken statically at the initial stage of the design. In addition, it allows migration and/or replication decisions to be taken by each cluster independently of other clusters using the proposed Optimal Fragment Reallocation and Replication (OFRAR) Algorithm. The proposed CB-DDBS architecture and the proposed OFRAR Algorithm are tested in both Amazon cloud environment and a simulated environment. Experimental results show that the proposed OFRAR Algorithm efficiently reduces the communication costs for typical access patterns, the overloads of the sites, and the frequency and time spent on fragment migration over the network sites by imposing a stricter condition for fragment reallocation and replication, resulting in a great overall improvement in the DDBS performance. It also shows that the proposed CB-DDBS architecture results in a significant reduction of the execution time needed for the transactions and for noticing an error.